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njwildberger.com | ||
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cre8math.com
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| | | | | This might sound like an odd question -- most students seem to think so when I ask it. The reason it sounds a little strange is that most students -- even when I taught at a magnet STEM high school -- think there's just one type of geometry: Euclidean geometry. This isn't surprising given the... | |
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carcinisation.com
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| | | | | Gödel's theorems say something important about the limits of mathematical proof. Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be "inside" the universe it's saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it's hard to make a proof of it using nothing... | |
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jdh.hamkins.org
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| | | | | This will be a series of lectures on the philosophy of mathematics, given at Oxford University, Michaelmas term 2018. The lectures are mainly intended for undergraduate students preparing for exam ... | |
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almostsuremath.com
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| | | The monotone class theorem is a very helpful and frequently used tool in measure theory. As measurable functions are a rather general construct, and can be difficult to describe explicitly, it is common to prove results by initially considering just a very simple class of functions. For example, we would start by looking at continuous... | ||
